On the Boltzmann equation for charged particle beams under the effect of strong magnetic fields

Mihai Bostan

doi:10.3934/dcdsb.2015.20.339

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2015, Volume 20, Issue 2: 339-371. Doi: 10.3934/dcdsb.2015.20.339

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On the Boltzmann equation for charged particle beams under the effect of strong magnetic fields

Mihai Bostan^1,

1.
Institut de Mathématiques de Marseille UMR 7353, Aix Marseille Université, CNRS, Centrale Marseille, 13453 Marseille

Received: September 2013

Revised: September 2014

Published: March 2015

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Abstract

The subject matter of this paper concerns the paraxial approximation for the transport of charged particles. We focus on the magnetic confinement properties of charged particle beams. The collisions between particles are taken into account through the Boltzmann kernel. We derive the magnetic high field limit and we emphasize the main properties of the averaged Boltzmann collision kernel, together with its equilibria.

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Mathematics Subject Classification: Primary: 35Q75, 82D10; Secondary: 78A35.

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